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<p>
Currently in the LMFDB, we have data on L-functions associated to
{{ KNOWL("mf.maass.mwf",title="Maass cusp forms")}} on
Hecke congruence groups 
$\Gamma_0(N)$ with character $\chi$. These L-functions \(L(s,f) = \sum a_n n^{-s} \) have an 
{{ KNOWL('lfunction.euler_product', title='Euler product')}}
of the form
\[
   L(s,f)= \prod_{p\mid N}  \left(1 - a_p p^{-s} \right)^{-1}\prod_{p\nmid N}  \left(1 - a_p p^{-s} + \chi(p)p^{-2s} \right)^{-1}
\]
and satisfies the 
{{ KNOWL("lfunction.functional_equation",title="functional equation")}} of the form
\begin{equation} 
\Lambda(s,f) = N^{s/2} \Gamma_{\mathbb{R} }
\left(s + iR \right) \Gamma_{\mathbb{R} }
\left(s - iR \right) \cdot L(s, f) =
\varepsilon \Lambda(1-s,f),
\end{equation}
where $N$ is the {{ KNOWL("mf.maass.mwf.level",title="level")}} and
$R$ the {{ KNOWL("mf.maass.mwf.eigenvalue",title="eigenvalue")}} of the
Maass cusp form.
</p>
<p>
The L-functions below are organized in terms of
level and eigenvalue.
</p>

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